Numerical Solution Of Induced Currents On Printed Wiring Boards

Abstract

Finite D@rence(FD) technique is applied to qirusi-TEM electronlagtietic fields to calculate induced currents on purullel truces of a printed wiring board and visualize c.ro.ss-sec.tioti~i1 electric und magnetic field vectors. The cwiipirter code was developed fo r iise in a MATLAB environnient, allowing portability and' exchange between various p1atforni.s running M A T U B . Open-boundary conditions are siniulated irsing Transparent Grid Termination (TGT) technique. Induced current data and vector plots are given for severul geometries involving printed wiring board truces positioned differently with respect to each other. Introduction The objectives are to calculate cuments and potentials induced on parallel traces of a printed wiring board (PWB) and visualize the electric and magnetic field clistribut.ions for PWB cross-sections. I t is assumed that there is no field variation with respect to one coordinate, the one in the direction of propagation, such that problem can be treated as two-dimensional (2-D). This is the s,o-called quasi-TEM approximation for inhomogeneous domains. Typical configuration we have analyzed involves, a dielectric substrate of known permittivity with two narrow PEC strips and a wider PEC ground plane. One strip is "active" with a known potential difference imposed between the strip andl the ground plane, as if the strip were driven by an ideal voltage source. The current on the active strip is not known, and depeinds on the impedance that the strip presents to the source. The other strip is "quiet"and neither its induced potential nor its induced current are known. The physical proximity of the quiet strip alters the current on the active strip and a current and a potential are induced on the quiet strip. The two strips are either in the same plane ("cdgc coupling"), or one of the strips is "buried" in the substr;ite. iis c;in bc the case with niulti-layered boards. 'l'lic induced current on the qiiiel strip is noriiwlized to the current on the active strip to obtain the "induced current cocflicient". Similarly, the induced volliige coefficient isdefined as the ratio of~t ie iritlucctl potenti:il on thc quiet strip to he potential ofthc xtivc strip. The two coefficients depend on the spacing between the strips, and decrease monotonically as the spacing is increased. We have investigated the dependence of these coefficients on the position and spacing of the strips. Nu me rical Tech n i a Standard Finite Difference technique is employed to calculated the potentials on a cross-section. A uniform, square FD grid is ussuined. Laplace's equation is solved in 2-D, subject to a simulated open-boundary condition and a known potential on the active strip. Since we have used well-known FD equations for the potentials, the FD details will be omitted. The system of FD equations, with proper source and boundary conditions, is solved for the unknown potentials. The potential solution is then used to find the electric field as the negative gradient of the potential. Electric field and the intrinsic impedance of the medium are used to find the magnetic field. In our calculations we selected a square computational grid with 31 by 31 nodes. The TGT is implemented for the outermost layer of the (31 by 31) computational grid. The particular TGT implementation we selected is for a grid "compression" of 101 to 31, which means that our calculations on a 3 I by 3 1 grid with the TGT give the same result as would calculations on a 101 by 101 grid with Dirichlet (zero potential) boundary condition for the outermost layer. The use of TGT allows for significant savings of computer memory and time. The way we simulate open boundary condition, which we refer to as the TGT, is (to our best knowledge) new and will be addressed next.